Methods resolving the elevation of a tracked personnel or assets

ABSTRACT

Methods and systems are described for determining the elevation of tracked personnel or assets (trackees) that can take input from mounted sensors on each trackee (including barometric, inertial, magnetometer, radio frequency ranging and signal strength, light and GPS sensors), external constraints (including ranging constraints, feature constraints, and user corrections), and terrain elevation data. An example implementation of this method for determining elevation of persons on foot is described. But this method is not limited to computing elevation of personnel or to on foot movements.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit under 35 U.S.C. §119(e) of ProvisionalU.S. Patent Application No. 61/658,883, filed Jun. 12, 2012, andProvisional U.S. Patent Application No. 61/783,799, filed Mar. 14, 2013,the contents of which are incorporated herein by reference in theirentireties.

GOVERNMENT RIGHTS

The subject matter disclosed herein was made with government supportunder award/contract/grant number W91CRB-09-C0089, awarded by the U.S.Army and W31P4Q-10-C-0166, awarded by the Defense Advanced ResearchProjects Agency. The Government may have certain rights in the hereindisclosed subject matter.

TECHNICAL FIELD

The present disclosure relates to systems and methods for trackingpersonnel or assets without the benefit of GPS sensors.

BACKGROUND

The present disclosure relates to algorithms and technology foreffective, accurate location, and tracking solutions in GPS deniedenvironments. Tracking systems for personnel or assets use a set ofinertial, magnetometer, pressure, and ranging sensors to providelocation estimates (and map buildings) when moving in GPS-deniedenvironments.

SUMMARY

A method has been developed and implemented to resolve the elevation oftracked personnel or assets (trackees) that can take input from mountedsensors on each trackee (including barometric, inertial, magnetometer,radio frequency ranging and signal strength, light and GPS sensors),external constraints (including ranging constraints, featureconstraints, and user corrections), and terrain elevation data. Animplementation of this method has been completed for determiningelevation of persons on foot but this method is not limited to computingelevation of personnel.

BRIEF DESCRIPTION OF THE DRAWINGS

Throughout the drawings, reference numbers may be re-used to indicatecorrespondence between referenced elements. The drawings are provided toillustrate example embodiments described herein and are not intended tolimit the scope of the disclosure.

FIG. 1 illustrates an example of a tracking system in a GPS deniedenvironment, according to an embodiment of the present disclosure;

FIG. 2 illustrates an example for creating stationary pressurereference, according to an embodiment of the present disclosure;

FIG. 3 illustrates an example of a standard building model, according toan embodiment of the present disclosure;

FIG. 4 illustrates an example plot for an input elevation in metersversus time with marked segments, according to an embodiment of thepresent disclosure;

FIG. 5 illustrates an example navigation frame—z acceleration data,according to an embodiment of the present disclosure;

FIG. 6 illustrates an example navigation frame—z acceleration afterbandpass filter, according to an embodiment of the present disclosure;

FIG. 7 illustrates an example Z Speed and estimated error, according toan embodiment of the present disclosure;

FIG. 8 illustrates an example vertical distance estimation, according toan embodiment of the present disclosure;

FIG. 9 illustrates an example vertical speed estimation using a singleintegrator, according to an embodiment of the present disclosure;

FIG. 10 illustrates an example vertical speed estimation using twointegrators, according to an embodiment of the present disclosure;

FIG. 11 illustrates an example inertial elevation aiding signal overtime, according to an embodiment of the present disclosure; and

FIG. 12 illustrates an example computing system, according to anembodiment of the present disclosure.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Wearable computing systems configured for tracking (e.g., waist worntracking systems, such as illustrated in FIG. 1) may use a set ofinertial, magnetometer, pressure, and ranging sensors to providelocation estimates (and map buildings) for personnel moving inGPS-denied environments (or other environments that are denied data fromsatellite positioning or navigation systems, e.g., Galileo). Onepossible implementation of the elevation method uses a computing deviceassociated with a user and a server. The user may be referred to astrackee and may be a personnel for which an elevation is determined; thecomputing device associated with the user may be referred as a trackeedevice. The elevation and other location data of the trackee maycorrespond to the elevation and other location data of the trackeedevice. The computing device may collect and transmit data to the serverthat, in turn, processes the data to generate an elevation. In anembodiment, the elevation method takes input data received from thecomputing device, such as TRX Systems Tracking Unit (e.g., a dynamictrackee device provided by TRX Systems), and another computing device,such as Multi-Sensor Anchor Nodes (e.g., a static device providingreference data). This data along with location constraints entered inthe Neon Command Station or Neon Handheld User Interface software, bothof which may be hosted on the server and may be provided by TRX Systems,provide the necessary information to accurately resolve a trackee'selevation. Once an absolute altitude is able to be determined, theserver, such as the Neon Elevation Engine (which may be provided by TRXSystems), uses the user entered building and terrain information tofurther determine the relative elevation from the terrain as well asfloor numbers suitable for display in the Neon Command Station software.

In the NEON system (e.g., a system provided by TRX Systems that compriseall or some of the elements described herein), 3-D location estimationmay be computed in 2 phases, first a 2-D location estimate is madeproviding a globally referenced location (longitude and latitude) andthen an elevation estimate is computed. These two segments of theprocessing may be independent; one can occur without the other. Thisdisclosure focuses only on the computation of globally referencedelevation (e.g., the second phase of the 3-D location estimation). Thiselevation engine could be combined with any mechanism for estimating 2-Dlocation.

Input Data

This method computes elevation for either static (a stationary referenceanchor) or dynamic (a movable tracked asset or individual) trackees. Italso provides adjustments to floor heights in building models. Severalinput data sources are considered when resolving the altitude of atrackee. These data sources are detailed in Table 1.

TABLE 1 Neon Elevation Engine Input Data Input Data Source Data Rate(Hz) Chirp Spread-Spectrum TRX Tracking Variable Ranging Unit/TRX AnchorWaypoint Check-in Android Phone Variable User Correction CommandStation/ Variable Android Phone Barometric Pressure Sensor TRX TrackingUnit/ Variable TRX Anchor (min 0.33 Hz) Terrain Elevation Data USGSBuilding Models NEON Command Station (or other)

In an embodiment, the method may collect ranging data from a ChirpSpread Spectrum RF ranging model. But the method is not limited to thisdata source. Instead, this data source is intended to represent datafrom any ranging source that can provide range to a known referencelocation/feature (for example, this could also come from an opticalsensor). The Waypoint Check-in and User Correction represent any manualsource of providing location/elevation data. The barometric pressuresensor represents any source of elevation data, for example, a laseraltimeter in an air vehicle. Terrain elevation data can be obtained frommany sources at varying resolutions. Building models provide floorfootprint data and some estimate of floor spacing. The floor spacing isadaptively updated by the algorithm.

Elevation Engine Cortices

The Neon Elevation Engine (e.g., implemented on a server) may bearranged into individual components (cortices) that can be executed inseries. A cortex is a small modular function block of code that can havealmost any task. For example, the cortex can be responsible forcalculating the properties of given data sets, filtering, or applyingconstraints. Each cortex can run in parallel with others or in series.The structure imposed on implementation of cortices allows them to beused as algorithm building blocks.

The first cortex, Create Elevation Ranges Cortex, can be responsible forextracting all data that can constrain a trackee's elevation within someerror bounds. Then the elevation global and local solvers, both of whichmay be implemented using Elevation Global Solver Cortex and ElevationLocal Solver Cortex, respectively, can use the filtered constraintsalong with additional raw sensor data to further resolve the absoluteelevation of the trackee.

Create Elevation Ranges Cortex

The create elevation ranges cortex can serve two primary functions. Itcan first identify static (non-moving) trackees with associated sensordata. The static trackees could be Multi-sensor Anchor Nodes, Waypoints,or NFC Check-in locations (as shown in FIG. 1) that are placed in theenvironment. Secondly, it can extract the distances between statictrackees and dynamic (moving) trackees.

When identifying static trackee location information, three distinctpieces of information may be available. This information may include aglobal location, floor number, and altitude as detailed in Table 2.These known values could be entered into the Neon Command Stationsoftware and may be associated with Waypoints, NFC Check-in locations,and Multi-sensor Anchor Nodes or estimated (which may be referred toherein as soft waypoints/check-ins or dropped anchors to differentiatethem from those with known location) by the NEON navigation engine. Onlystatic trackees that have at least one piece of position information maybe considered. As dynamic trackees traverse the world, they may check-inat waypoints and NFC check-in locations, and collect ranging databetween themselves and other static and dynamic trackees.

TABLE 2 Static Trackee Position Information Static Trackee PositionInformation Details Global Location Latitude and Longitude Known FloorNumber Floor number Known Altitude Altitude in meters above sea level

Once all known static trackees have been determined, the CreateElevation Ranges cortex may extract distance constraints between each ofthe static trackees and other dynamic trackees. These constraints can becreated in response to measured sensor data or user actions (forexample, Table 3).

TABLE 3 Elevation Engine Ranging Constrains Constraint Type ValueLocation Information Chirp Spread-Spectrum distance with Relativedistance Ranging error between trackees Waypoint Check-in 0 meterdistance Absolute location User Correction 0 meter distance Absolutelocation to floor or altitude

In this embodiment, 0 meter distance constraints can be used forwaypoints check-ins and user corrections, but these could be other fixedvalues or even variable values potentially entered by the user (e.g.,the trackee).

Elevation Global Solver Cortex

The Elevation Global Solver can perform a global optimization over givenconstraints to solve for trackee elevation. The main function of thesolver may be to determine the computation of global offsets for eachtrackee. However, to do this, the global solver may first solve for apressure reference that is needed in order to remove local atmosphericpressure variation.

Since a barometric pressure sensor can be used as an input, it may benecessary to remove local atmospheric pressure variation; this variationis present both inside and outside of buildings. Additionally, eachdevice can have a significant offset relative to other devices. Whilebarometric pressure sensors often have a precise resolution and thusprecise relative accuracy when looking at the data from a single sensor,they can suffer from a poor absolute accuracy and can show significantsensor to sensor variation. In practice this sensor to sensor offset canresolve to an elevation error of multiple floors between two trackees ifoffsets are not properly resolved. The datasheet information for thepressure sensor used in the TRX Tracking Unit (or any dynamic trackeedevice) is listed below in Table 4.

TABLE 4 TRX Tracking Unit Barometric Pressure Sensor DatasheetInformation Parameter Value (mbar) Value (Pa) Distance (m, sea level)Resolution 0.012 1.2 0.09989 Accuracy ±01.5 ±150 ±12.494

In order to correct for local atmospheric pressure variation, astationary pressure reference algorithm can be used to fuse the pressuredata from all static trackees into a single 0-based stationary pressurereference, as further described herein below. Data can be collected frommultiple static trackees as various data rates. An assumption can bemade that all static trackees will experience the same local atmosphericpressure variation, which has been observed to be a sufficiently goodapproximation in practice when tracking over a relatively small area(e.g., an area corresponding to a few travelled miles).

Given constraints to static trackees with known elevations, constraintsbetween dynamic trackees, and stationary pressure reference correctionsto trackee pressure data, an iterative solver can be used to determinethe offsets per dynamic trackee that satisfies the most constraintspossible. An assumption is made that constraints can be satisfied byapplying a single offset to the corrected pressure for each trackee.

Stationary Pressure Reference

The stationary pressure reference is a measure of the local atmosphericvariation of pressure. It can be used to compensate for pressurevariation that is not due to a change in elevation. The stationarypressure reference is created using data combined from static trackeesin a local area. FIG. 2 shows pictorially the concept of combiningpressure data from sensors with potentially unknown elevation to derivea measure of pressure variation.

To create the stationary pressure reference, time correlated pressuredata may be required from static trackees. This data can then be storedin bins separated by 2 seconds (or another similar time interval). Aseach new static trackee pressure is added to the stationary pressurereference data structure, the offset for that static trackee can bedetermined. The computed offset can be a combination of the deviceoffset and any fixed elevation offset resulting from the location of thedevice.

The first static trackee data received can be given an offset equal totheir measured pressure and thus the first pressure reference value canbe 0 (this is a 0-based data structure, although other data structuresmay be use and other references may be used for this data structure orother data structures. Offsets for all subsequent static trackee's canbe calculated relative to the stationary pressure reference. Thestationary pressure reference structure can adjust for the offset foreach static trackee before adding samples to the reference pressurestructure.

When static trackee pressure data with an unknown offset is deposited,its offset can be resolved using the following rules:

-   -   1. If there is no stationary pressure reference data        -   Offset=0    -   2. If the input time is less than the first stationary pressure        reference time (assume that the pressure was constant prior to        that time)        -   Offset=first stationary pressure reference pressure−static            trackee pressure data    -   3. If the input time is greater than the last stationary        pressure reference time (assume that the pressure was constant        after that time)        -   Offset=last stationary pressure reference pressure−static            trackee pressure data    -   4. Otherwise        -   Offset=last stationary pressure reference pressure with time            less than input time−static trackee pressure data.

Once the offset has been determined, the offset adjusted pressurereference data (Offset−static trackee pressure data) can be stored intothe 2-second bins (or any other bins corresponding to the used timeinterval). Each 2-second bin may keep track of all pressure valuesdeposited into the bin. There may be one or many pressure values withineach bin. Since pressure reference data may be from trackees that arenot moving, if there are any periods of missing data, the pressure dataover those periods can be assumed constant. In the end, each bin can beaveraged to create a unified stationary pressure reference signal. Thistakes advantage of all static trackee pressure values and can produce amore consistent estimate of the atmospheric pressure drift by averagingover all static trackees.

When the elevation global solver needs to reference the stationarypressure reference, a method can be used to query the stationarypressure reference data at a particular point in time. This method canreturn a pressure value at a particular time using the following rules:

-   -   1. If there is no pressure reference data        -   pressure reference=0    -   2. If the input time is less than the first stationary pressure        reference time        -   pressure reference=first stationary pressure reference            pressure    -   3. If the input time is greater than the last stationary        pressure reference time        -   pressure reference=last stationary pressure reference            pressure    -   4. Otherwise        -   pressure reference=linearly interpolated stationary            reference pressure between closest points by time.

Adjusted Pressure

Once the stationary pressure reference has been determined, each dynamictrackee's pressure can be adjusted to account for atmospheric drift. Thecorrected pressure, p(t), can be calculated by subtracting thestationary reference pressure from the dynamic trackee's pressure. Thecompensated signal can then be filtered using a window filter to removeany noise. This could be any smoothing filter. Since pressure data maynot be uniformly sampled, the number of future and past data samples maynot be guaranteed to be equal. To better handle the non-uniformity ofthe data, in an embodiment, the windowed filter can be implemented suchthat it may equally weight prior data, current data, and future data inthe smoothing filter irrelevant of the number of available data points.As an example, a window around the current data point of 10 seconds, ±5seconds, is used. The filtered pressure, f(t), can be given by:

${f(t)} = \frac{{{p(t)}*\left( {1 + {{l(t)}*{r(t)}}} \right)} + \left( {\sum\limits_{{p{(i)}} \in L_{t}}\left( {{p(i)}*{r(t)}} \right)} \right) + \left( {\sum\limits_{{p{(i)}} \in R_{t}}\left( {{p(i)}*{l(t)}} \right)} \right)}{1 + {3*{l(t)}*{r(t)}}}$

-   p(t)={input pressure}-   L_(t)={pressure values between t−5 and t}-   R_(t)={pressure values between t and t+5}-   l(t)={number of values between t−5 and t}-   r(t)={number of values between t and t+5}.

Generate Constraints

Once a filtered dynamic trackee pressure signal is available for eachdynamic trackee, elevation constrains can be created to be used in theelevation global solver. Each constraint type may contain a costfunction and a gradient of the cost function. The constraints can besolved by iteratively minimizing the cost function. The solver mayattempt to lower the cost of each constraint to 0. The gradients can beused to determine how to shift the pressure in the z direction tominimize the total cost. Overall, the global solver can be responsiblefor determining the z offset for each dynamic trackee.

The first type of constraint is an altitude elevation constraint; thisis a constraint between a dynamic trackee elevation and a static trackeeelevation. This constraint can be created when a dynamic trackee gets arange measurement to a static trackee. In addition to the rangemeasurement, the static trackee may have knowledge of either its floornumber or its geo-referenced elevation (e.g. height above the earthreference ellipsoid WGS-84). When geo-referenced elevation is notavailable, the user entered building model can be used to calculate theelevation based on the local terrain elevation information and buildinginformation including floor number. Local terrain elevation data isavailable from U.S. Geological Survey (USGS) in the United States. Iflocal terrain data is not available, the ground level immediatelyoutside of a building can be assumed to be 0 elevation. Away from thebuilding the elevation will track relative elevation based on dataavailable from pressure. In this case, there may not be enoughinformation to automatically handle multilevel entrances or multiplebuildings in non-flat terrain. The cost and gradient functions for thealtitude elevation constraint can be given by:

${cost} = \left\{ {{\begin{matrix}\left( {e + r} \right)^{2} & {e < {- r}} \\\left( {e - r} \right)^{2} & {e > r} \\0 & {otherwise}\end{matrix}{gradient}} = \left\{ {{\begin{matrix}{- 1} & {e < {- r}} \\1 & {e < r} \\0 & {otherwise}\end{matrix}e} = {p + o - a}} \right.} \right.$

-   -   r={range constraint}    -   a={static trackee altitude}    -   p={dynamic trackee pressure}    -   o={calculated offset}.

The second type of constraint is a trackee to trackee elevationconstraint. This constraint is created between the elevations of twodynamic trackees. The benefit of this constraint can be that as moredynamic trackees are created, they can help each other better resolvetheir global offset by using the ranging data shared between them. Theseconstraints should have lower weight than the static constraints so thecost can be multiplied by a weight such that the sum of all trackee totrackee constraints is equal to 0.1*number of static constraints (or asimilar weight). The cost and gradient functions for the trackee totrackee elevation constraint can be given by:

${cost} = \left\{ {{\begin{matrix}{w*\left( {e + r_{kj}} \right)^{2}} & {e < {- r_{kj}}} \\{w*\left( {e - r_{kj}} \right)^{2}} & {e > r_{kj}} \\0 & {otherwise}\end{matrix}{gradient}} = \left\{ {{\begin{matrix}{- w} & {e < {- r_{kj}}} \\w & {e > r_{kj}} \\0 & {otherwise}\end{matrix}e} = {\left( {p_{k} + o_{k}} \right) - \left( {p_{j} + o_{j}} \right)}} \right.} \right.$

$w = {0.1*\frac{n_{s}}{n_{p\; 2p}}}$

{person to person constraints weight}

-   -   n_(s)={the number of static constraints}    -   n_(p2p)={the number of person to person constraints}    -   r_(kj)={range between dynamic trackee k and j}    -   p_(k)={pressure of dynamic trackee k}    -   o_(k)={calculated offset of dynamic trackee k}.

Solve Constrains

The elevation global solver can be configured as a robust iterativeconstraint solver. It may first loop through all constraints by trackee,attempting to find the best offset for each trackee. Once an offset hasbeen computed for each trackee, if the sum of the costs is lower thanthe best known cost, then the offset can be changed to the new value.This type of iterative constraint solvers can typically be iterateduntil they reach a maximum number of iterations or the cost decrease perstep is below a threshold.

A more detailed description of the algorithm is provided below in pseudocode as an example:

for (i = 0; i < iterations; i++) {    for (j = 0; j < numTrackees; j++)   {       gradient = sum of gradients for trackee j;       offset =(gradient > 0) ? previousOffset − step :       reviousOffset + step;      cost = sum of all costs for trackee j;       if (cost < lastCost)         step *= 1.2;       if (cost > lastCost)          step *= 0.8;      lastCosts[j] = cost;       lastOffsets[j] = offset;    }   lastCosts = sum of costs of all trackees for last iteration;   bestCosts = sum of costs of all trackees for lowest cost iteration;   if (lastCosts < bestCosts)    {       bestCosts = lastCosts;      bestOffsets = lastOffsets;    } }

Once the offset for each dynamic trackee has been determined, theresolved elevations can be forwarded to the elevation local solver tohandle smaller local changes.

Elevation Local Solver Cortex

The elevation local solver can resolve the final elevation of a dynamictrackee. The Indoor path points for dynamic trackees can be broken intostable segments and unstable segments. Constraints to static trackeesand other dynamic trackees can be used again. Buildings can be includedin the solver, where floor heights can be adaptively adjusted in orderto solve constraint conditions. Terrain data can be included for outdoorpath points. A single iterative particle solver can be used to resolvethe final elevation per dynamic trackee and the final adjusted floorheights of buildings. A particle solver is a standard mechanism inphysics and computer graphics of repeatedly iterating through a seriesof constraints until a solution that “best” satisfies the constraints isreached

Building Model

Each building that contains any part of any trackees locations can beincluded in the particle solver. A building has floors with set heightsabove the ground level. Each floor has a known absolute elevation. Asimple model is used in FIG. 3 as an example. However, the samealgorithm could apply to a variety of building models that may includemore complex models.

The default building model can assume that every basement level has thesame floor height as other basement levels, the ground level has its ownunique height, and the levels higher than the ground level all have thesame floor height as other above ground levels. FIG. 3 shows thestandard building model, with levels assumed to have the same heights inthe same color.

The particle solver can adjust the height of each floor when satisfyingconstraints. The building model can have its own solve mechanism. Allfloors that are modified by the solver can be used to calculate thebelow ground floor height, ground floor height, and above ground floorheight. If the ground floor is modified, the value can simply be kept.If any floors below ground are modified, the average floor height can beestimated and then applied to all floors below ground. If any aboveground floors are modified and the ground floor itself is already set, asimple average can be estimated and applied to the above ground floors.If the ground floor has not been modified, a linear regression can beused such that the offset component of the linear regression is theground floor height, and the slope is the above ground floor height.

Path Segmentation

The input path for each dynamic trackee can be segmented and theendpoints of the segments can be set as nodes for the particle solver.An example mechanism that the particle solver uses to act on each nodetype is described in the next section.

The segmentation of the path can proceed as follows: the input elevationcan be parsed in order of ascending time. All points that are indoorsand considered stable can be grouped into a single segment. Below is theformula for determining if a point may be considered stable. The methodchecks for elevation changes on the left and right of the current pointand if either side is flat, the point may be considered to be stable.

stable(t) = leftStable(t)  OR  rightStable(t)${{leftStable}(t)} = {{{\max\left( {{\max\limits_{{p{(i)}} \in L_{t}}\left( {p(i)} \right)},{\overset{\sim}{p}\left( {t - 8} \right)}} \right)} - {\min\left( {{\min\limits_{{p{(i)}} \in L_{t}}\left( {p(i)} \right)},{\overset{\sim}{p}\left( {t - 8} \right)}} \right)}} < {{- 0.5}\mspace{14mu} m}}$${{rightStable}(t)} = {{{\max\left( {{\max\limits_{{p{(i)}} \in R_{t}}\left( {p(i)} \right)},{\overset{\sim}{p}\left( {t - 8} \right)}} \right)} - {\min\left( {{\min\limits_{{p{(i)}} \in R_{t}}\left( {p(i)} \right)},{\overset{\sim}{p}\left( {t - 8} \right)}} \right)}} < {0.5\mspace{14mu} m}}$

-   p(t)={input elevation}-   {tilde over (p)}(t)={linearly interpolated input elevation}-   L_(t)={elevation values between t−8 s and t}-   R_(t)={elevation values between t and t+8 s}

Once the input elevation is segmented in to stable indoor segments,outdoor segments can be added every 10 seconds while outdoors, andunderground segments are added every 10 seconds while not outdoors andnot in a building. Other similar time intervals may also be used. FIG. 4shows sample input elevation with path segments shown as black flatlines. The units are in meters versus time, and the segments are storedas a start and end time with an average elevation as shown on the plot.

Inertial Aiding

Pressure anomalies that are not caused by change in elevation on entryor exit from buildings can be observed in certain situations such aswhen the tracking system is used with firefighters near a fire. If highsample rate vertical accelerometer information is available to thesystem, the inertial data can be used to aid in filtering out pressureanomalies.

The z-axis accelerometer measures vertical acceleration. When there is atrue elevation change, there are variations in the vertical accelerationand velocity. The vertical velocity can be computed by:

-   -   1. transforming the accelerometer data into the earth frame        (tilt compensation);    -   2. filtering the (z-axis) accelerometer data with a band pass        filter to remove constant effect of gravity and high frequency        noise; and    -   3. integrating the tilt compensated and filtered (z-axis)        accelerometer data.        If vertical velocity breaks a threshold, then a “vertical        counter” can be incremented to indicate that a vertical change        has occurred.

Using this aiding information, the path constraints between pathsegments (of all types) can be modified to eliminate pressure variationthat may not be related to elevation change. If there is no change inthe vertical counter over a segment, the constraint can be changed toindicate 0 elevation difference over the segment instead of using theelevation change based on pressure.

To demonstrate this method, an example test path is described hereinbelow and is run through the algorithm in detail.

Test Path

-   -   Starting at 4^(th) floor SE exit, walk to end of hall and then        upstairs at normal speed to 5^(th) floor.    -   Walk across 5^(th) floor to stairwell and return to 4^(th) at        normal speed.    -   Walk across 4^(th) to stairwell and go up at fast speed to        5^(th).    -   Walk across 5^(th) floor to stairwell and return to 4^(th) at        fast speed.    -   Walk across 4^(th) to stairwell and go up at slow (one step at a        time)speed to 5^(th).    -   Walk across 5^(th) floor to stairwell and return to 4^(th) at        slow speed.    -   Walk to 4^(th) floor elevator and go down to 1^(st).    -   Walk around lobby and then take elevator back to 4^(th).

Algorithm

Sample Z acceleration data in navigation frame (an example is shown inFIG. 5) can be processed using the following algorithm:

-   -   1. Subtract 1000 mg gravitation acceleration from Z-acceleration        sample.    -   2. Pass result of (1) through band pass filter (CUTOFF _(—)        LOWER=0.01, CUTOFF _(—) UPPER=0.25). An example output of this        step is shown in FIG. 6.    -   3. For each sample, if the absolute value of the sample is        greater than threshold level ACTIVATION _(—) THRESH _(—) MG,        enable integration of filtered acceleration signal and error        signal which represents the maximum integration error due to        poor calibration and noise (fixed to 3 mg per sample in this        case). In short, the vertical speed is being clamped to zero for        all times when the acceleration is near zero.    -   4. Once the acceleration integration result falls below the        error integrator value, stop the integration. The result        represents the vertical speed of the user. An example output of        this step is shown in FIG. 7; the Z Speed is shown using a        dotted line and the estimated error using a solid line. See        “Benefits of 2 Integrators” below for more information.    -   5. Integrate result to compute distance. An example output of        this step is shown in FIG. 8.

Accelerometer Offset Detection

It is very important that the accelerometer be calibrated well for thisalgorithm to work correctly. An offset detection algorithm can be usedto refine Z-acceleration offset over time. This algorithm can involvethe following listed steps.

-   -   1.) When the integrators are not active, filtered acceleration        samples are accumulated. A counter is incremented for each        sample accumulated.    -   2.) When the integrator becomes active, the sample counter is        checked to ensure at least 10 seconds (or other time interval)        of data has been accumulated.    -   3.) If enough data has been collected the z offset parameter is        updated to be the average of all samples accumulated.

Benefit of 2 Integrators

If one integrator is used and stops integration too early, a secondaryintegrator that has continued integrating can help to preventovershooting of integration as it returns to zero and provide betterdistance estimates (especially after, for example, a stair landing). Inthis embodiment, Integrator1 and Integrator2 start at zero and areenabled when the filtered acceleration value crosses a threshold.Integrator1 (e.g., the first integrator) can be stopped when the resultfalls within the integrator error estimate; integrator2 (e.g., thesecond integrator) can continue to integrate until it is reset by alater elevation event.

If a second elevation event is detected shortly after (within about 2seconds or a similar time interval) the end of a previous elevationevent, the first integrator can be initialized at the value of thesecondary integrator instead of being initialized to zero. Theimprovement gained is shown in FIG. 10 in comparison to FIG. 9 (comparethe integrated acceleration data between samples 3100 and 3200). In FIG.9, the estimated error is shown using a dotted line. In both FIGS. 9 and10, the Z speed is shown using a solid line. As is shown in FIG. 10, theZ speed has a reduced overshoot as a result of using two integrators.

Selecting Band Pass Filter Cutoffs

The algorithm is not very sensitive to the lower cutoff threshold. Infact a simple low-pass filter may still work fairly well. The highcutoff and the threshold used for integrator activation work together todetermine the types of elevation changes that may be detected.

Example of Integrated Signal with Mean Value Removed

Referring to FIG. 11, that figure illustrates the inertial elevationaiding signal (e.g., Z acceleration) over time. As shown in this figure,even with post-processing, completely removing the large low frequencycomponent may be difficult.

MATLAB Code for Inertial Elevation Aiding Estimate

% Constants ACTIVATION_THRESH_MG  =(25); ZV2_RESET_TIME   =(2);INTEGRATION_TIMEOUT  =(10); ACCEL_ERROR_MG   =(3);INPUT_SAMPLE_PERIOD  =(0.025); % Filter cutoff CUTOFF_LOWER   =(0.01);CUTOFF_UPPER   =(0.25); FILT_SAMPLE_RATE   =(40); % Remove Accelerationdue to gravity zz = az − 1000; % Bandpass filter input signal zz =[zeros(1,63) zz′]; zz = zz′; b = fir1(63, [CUTOFF_LOWER/FILT_SAMPLE_RATECUTOFF_UPPER/FILT_SAMPLE_RATE], ‘bandpass’, blackman(63+1)); zfilt =conv(b, zz); % Workspace variables enableIntegration = 0; v1 = 0;   % Zintegrator 1 v2 = 0;   % Z integrator 2 lastEndSample = 0;lastStartSample = 0; zerror = 0; offset = 0; % Estimate of zacceleration offset (i.e. calibration) zsum = 0; zcount = 0; distance =0; % Start main loop for i = 1:length(zfilt)  s = zfilt(i) − offset; if(enableIntegration == 1)   if ((abs(v1) < zerror) && (abs(s) <ACTIVATION_THRESH_MG))    enableIntegration = 0;    v1 = 0;    zerror =0;    lastEndSample = i;   else    v1 = v1 + s*INPUT_SAMPLE_PERIOD;%Integrator 1 Update    v2 = v2 + s*INPUT_SAMPLE_PERIOD; %Integrator 2Update    zerror = zerror + ACCEL_ERROR_MG * INPUT_SAMPLE_PERIOD;%ErrorIntegrator   end   % Stop integrating after 2 seconds   if(((i-lastStartSample) > INTEGRATION_TIMEOUT*FILT_SAMPLE_RATE) && (abs(s)< ACTIVATION_THRESH_MG))    enableIntegration = 0;    v1 = 0;    v2 = 0;   zerror = 0;    lastEndSample = 0; % Errored out.. so invalidate   end elseif(enableIntegration == 0)   if(abs(s) > ACTIVATION_THRESH_MG)%Condition that enables integrator    enableIntegration = 1;   lastStartSample = i;    %If 400 samples have been collected, averageto estimate sensor offset    if(zcount > 400)     offset = zsum /zcount;    end    % If this activation is within 2 sec of last then pickup    % integration from z2. Otherwise restart bot integrators.    if(i-lastEndSample) < (ZV2_RESET_TIME * FILT_SAMPLE_RATE)     v1 =v2+s*INPUT_SAMPLE_PERIOD;    else     v1 = s*INPUT_SAMPLE_PERIOD;     v2= v1;    end    % Reset averaging logic    zcount = 0;    zsum = 0;  else    % This is the idle (not integrating case)    % Ignorebeginning 200 samples and accumulate the rest    if(i>200)     zsum =zsum + zfilt(i);     zcount = zcount + 1;    end   end  end  distance =distance+v1*INPUT_SAMPLE_PERIOD; end

Generate Constraints and Nodes

The iterative particle solver uses nodes and constraints. Certain nodeshave special properties such as:

-   -   path indoor and stable nodes attempt to snap to a floor in a        building;    -   path outdoor nodes try to snap to the outdoor terrain; and    -   fixed floor nodes may directly affect building floor locations.

All constraints may enforce a minimum and maximum allowed difference inelevation. For example, a received range of 3 meters from a fixed anchorat elevation z would enforce elevation min of z−3 and max of z+3. Thedifference in elevation can be positive or negative depending ondirection. Each dynamic node can have a cost, snap, and solve mechanismthat is utilized in the particle solver. Each constraint can have a costand solve mechanism.

Fixed Altitude Node

This node is used for constraints to static trackees that are at a knownaltitude. This node has no cost, no solve mechanism, and no snapping. Itcannot be moved and is a fixed point. It is used as an anchor in thesolver.

Fixed Floor Node

This node is used for constraints to static trackees that are on a knownfloor. It is attached to a Floor from the building model. The cost ofthis node may be set as the square distance in meters away from theattached floor. The snapping mechanism may set the elevation of thisnode equal to the elevation of the attached floor from the buildingmodel. The solve mechanism may move the node 50% (or another similarpercentage) toward the attached floor, and move the attached floor 50%(or a similar percentage complimentary to the other percentage such thatthe sum of both percentages is near or equal 100%) toward the node.

Path Indoor and Stable Node

This node is used for stable indoor path segments. It has no knownfloor, but is assumed to be attached to a floor in the building model.The cost of this node may be set as the square distance in meters awayfrom the closest current floor in the building model. The snap mechanismmay set the elevation of this node equal to the nearest floor if thenode is within 35% of the floor height in the building model. The solvemechanism may pull the nearest floor 50% (or another similar percentage)toward the node. If the node was within 35% of the floor height in thebuilding model, the node is moved 50% toward the floor (or a similarpercentage complimentary to the other percentage such that the sum ofboth percentages is near or equal 100%).

Path Outdoor Node

Outdoor path nodes are for path points of dynamic trackees that are notin buildings and not underground. The node references the terrain datato determine surface elevation. The cost, snap, and solve mechanism ofthis node may depend on whether the node is within 2 m of the terrain.If the node is not within 2 m, there may be no cost, snap, or solvefunctionality; the elevation is not affected by the solver. This, forexample, enables a trackee to walk across a bridge without being snappedto the ground. If it is within 2 m, the cost may be set as the squaredistance away from the terrain. The snap mechanism may set the nodeelevation equal to the terrain. The solve mechanism may set the nodeelevation to the terrain.

Path Underground Node

An assumption is made that there is no known underground map, otherwisea building structure would be added and the underground node would betreated as a basement level of a building. Without a map, a PathUnderground Node may be affected by constraints, but may have no othercost, snap, or solve mechanism. Unlike a Fixed Altitude node, this nodecan be moved by constraints.

Path Constraint

This constraint can only be created between two path nodes. Path nodesoccur in order over time and can be indoor, outdoor, or underground. Thedifference in elevation between these nodes, as indicated from the inputdata from the previous cortex, is the constraint difference. Therelative elevation of the nodes should remain the same as the originalinput. The cost may be set as the difference between the actual distanceand desired distance of the nodes squared. If the actual distance fallswithin the allowed range, there may be no cost. The solve mechanism maypush or pull each node 50% (or another similar percentage) toward thedesired distance. If one of the nodes is locked, the unlocked node maybe moved 100% of the way.

Range Constraint

This constraint occurs between a path node and a fixed node and iscreated from the input constraints. If the direction of the differencein elevation between nodes is not provided, the absolute value of thedifference must be constrained to be less than a certain range. The costof this constraint may be set as the difference between the maximumrange and the actual elevation difference squared. If the actualelevation difference is less than the maximum range then there may be nocost. The solve mechanism may pull each node 50% (or a similarpercentage) toward each other to satisfy being within the maximum range.If one node is locked, the other moves 100% of the way to satisfy themaximum allowed distance.

Trackee to Trackee Constraint

This constraint occurs between path nodes from different people. It iscreated from the input constraints. The direction of the difference inelevation may not be provided, only the absolute values may be given.The cost and solve mechanism may be identical to range constraints.

Solve Constraints

The particle solver may contain nodes and constraints between nodes. Theprevious section described the cost estimating, solving and snappingmechanism. The solver may include a combination of these nodes andconstraints. The solve algorithm can be set as follows:

function Solve( ) {    for 1..10    {       for 1..100       {         foreach Constraint in SolveConstraints          {            Constraint.Solve( )          }          foreach Node inSolverNodes          {             Node.Solve( )          }       }      foreach Building in SolverBuildings       {         Building.SolveFloorHeights( )       }       cost = 0      foreach Constraint in SolverConstraints       {          cost +=Constraint.Cost( )       }       foreach Node in SolverNodes       {         cost += Node.Cost( )       }       if cost < 0.1       {         exit       }    }    foreach Node in SolverNodes    {      Node.Snap( )    } }

The particle solver may iterate through each constraint and node, fullyresolving the constraints by locally moving the path. By iteratingthrough all the nodes and constraints, the system may settle to areasonable answer. A dampening factor can be applied to all the node andconstraint solve mechanisms to reduce potential oscillations. The finalstep of the solver can include a step to snap each node to a buildinglevel or outdoor terrain if applicable. The nodes represent a sampledversion of the full path elevation, so after each node has been given afinal elevation, the full path input elevation can be fitted to thenodes. The input signal can be either set to a constant value in thecase of indoor path nodes, or scaled and translated for all other nodes.The final result can be a set of elevation points over time that agreeswith the final nodes from the particle solver.

The techniques described above can be implemented on a computing deviceassociated with a user, a plurality of computing devices associated witha plurality of users, a server in communication with the computingdevice(s), or a plurality of servers in communication with the computingdevice(s). Additionally, the techniques may be distributed between thecomputing device(s) and the server(s). For example, the computing devicemay collect and transmit raw data to the server that, in turn, processthe raw data to generate an elevation. FIG. 12 describes a computingsystem that includes hardware modules, software module, and acombination thereof and that can be implemented as the computing deviceand/or as the server.

In a basic configuration, the computing system may include at least aprocessor, a system memory, a storage device, input/output peripherals,communication peripherals, and an interface bus. The interface bus isconfigured to communicate, transmit, and transfer data, controls, andcommands between the various components of the electronic device. Thesystem memory and the storage device comprise computer readable storagemedia, such as RAM, ROM, EEPROM, hard-drives, CD-ROMs, optical storagedevices, magnetic storage devices, flash memory, and other tangiblestorage media. Any of such computer readable storage medium can beconfigured to store instructions or program codes embodying aspects ofthe disclosure. Additionally, the system memory comprises an operationsystem and applications. The processor is configured to execute thestored instructions and can comprise, for example, a logical processingunit, a microprocessor, a digital signal processor, and the like.

The system memory and the storage device may also comprise computerreadable signal media. A computer readable signal medium may include apropagated data signal with computer readable program code embodiedtherein. Such a propagated signal may take any of variety of formsincluding, but not limited to, electro-magnetic, optical, or anycombination thereof. A computer readable signal medium may be anycomputer readable medium that is not a computer readable storage mediumand that can communicate, propagate, or transport a program for use inconnection with the computing system.

Further, the input and output peripherals include user interfaces suchas a keyboard, screen, microphone, speaker, other input/output devices,and computing components such as digital-to-analog and analog-to-digitalconverters, graphical processing units, serial ports, parallel ports,and universal serial bus. The input/output peripherals may be connectedto the processor through any of the ports coupled to the interface bus.

The user interfaces can be configured to allow a user of the computingsystem to interact with the computing system. For example, the computingsystem may include instructions that, when executed, cause the computingsystem to generate a user interface that the user can use to provideinput to the computing system and to receive an output from thecomputing system. This user interface may be in the form of a graphicaluser interface that is rendered at the screen and that is coupled withaudio transmitted on the speaker and microphone and input received atthe keyboard. In an embodiment, the user interface can be locallygenerated at the computing system. In another embodiment, the userinterface may be hosted on a remote computing system and rendered at thecomputing system. For example, the server may generate the userinterface and may transmit information related thereto to the computingdevice that, in turn, renders the user interface to the user. Thecomputing device may, for example, execute a browser or an applicationthat exposes an application program interface (API) at the server toaccess the user interface hosted on the server.

Finally, the communication peripherals of the computing system areconfigured to facilitate communication between the computing system andother computing systems (e.g., between the computing device and theserver) over a communications network. The communication peripheralsinclude, for example, a network interface controller, modem, variousmodulators/demodulators and encoders/decoders, wireless and wiredinterface cards, antenna, and the like.

The communication network includes a network of any type that issuitable for providing communications between the computing device andthe server and may comprise a combination of discrete networks which mayuse different technologies. For example, the communications networkincludes a cellular network, a WiFi/broadband network, a local areanetwork (LAN), a wide area network (WAN), a telephony network, afiber-optic network, or combinations thereof. In an example embodiment,the communication network includes the Internet and any networks adaptedto communicate with the Internet. The communications network may be alsoconfigured as a means for transmitting data between the computing deviceand the server.

The techniques described above may be embodied in, and fully orpartially automated by, code modules executed by one or more computersor computer processors. The code modules may be stored on any type ofnon-transitory computer-readable medium or computer storage device, suchas hard drives, solid state memory, optical disc, and/or the like. Theprocesses and algorithms may be implemented partially or wholly inapplication-specific circuitry. The results of the disclosed processesand process steps may be stored, persistently or otherwise, in any typeof non-transitory computer storage such as, e.g., volatile ornon-volatile storage.

The various features and processes described above may be usedindependently of one another, or may be combined in various ways. Allpossible combinations and sub-combinations are intended to fall withinthe scope of this disclosure. In addition, certain method or processblocks may be omitted in some implementations. The methods and processesdescribed herein are also not limited to any particular sequence, andthe blocks or states relating thereto can be performed in othersequences that are appropriate. For example, described blocks or statesmay be performed in an order other than that specifically disclosed, ormultiple blocks or states may be combined in a single block or state.The example blocks or states may be performed in serial, in parallel, orin some other manner. Blocks or states may be added to or removed fromthe disclosed example embodiments. The example systems and componentsdescribed herein may be configured differently than described. Forexample, elements may be added to, removed from, or rearranged comparedto the disclosed example embodiments.

Conditional language used herein, such as, among others, “can,” “could,”“might,” “may,” “e.g.,” and the like, unless specifically statedotherwise, or otherwise understood within the context as used, isgenerally intended to convey that certain embodiments include, whileother embodiments do not include, certain features, elements, and/orsteps. Thus, such conditional language is not generally intended toimply that features, elements and/or steps are in any way required forone or more embodiments or that one or more embodiments necessarilyinclude logic for deciding, with or without author input or prompting,whether these features, elements and/or steps are included or are to beperformed in any particular embodiment. The terms “comprising,”“including,” “having,” and the like are synonymous and are usedinclusively, in an open-ended fashion, and do not exclude additionalelements, features, acts, operations, and so forth. Also, the term “or”is used in its inclusive sense (and not in its exclusive sense) so thatwhen used, for example, to connect a list of elements, the term “or”means one, some, or all of the elements in the list.

While certain example embodiments have been described, these embodimentshave been presented by way of example only, and are not intended tolimit the scope of the inventions disclosed herein. Thus, nothing in theforegoing description is intended to imply that any particular feature,characteristic, step, module, or block is necessary or indispensable.Indeed, the novel methods and systems described herein may be embodiedin a variety of other forms; furthermore, various omissions,substitutions and changes in the form of the methods and systemsdescribed herein may be made without departing from the spirit of theinventions disclosed herein. The accompanying claims and theirequivalents are intended to cover such forms or modifications as wouldfall within the scope and spirit of certain of the inventions disclosedherein.

What is claimed:
 1. A computer-implemented method for determining anelevation of a tracked computing device in an environment, the methodbeing executed on a server and comprising: determining a location of astatic computing device; determining an offset associated with thestatic computing device, the offset being indicative of an atmosphericpressure at the static computing device; estimating the atmosphericpressure associated with the tracked computing device based on theoffset and on information received from the tracked computing device;and generating the elevation of the tracked computing device based onthe atmospheric pressure associated with the tracked computing device.2. The method of claim 1, wherein the static computing device is asensor node installed at a known location in the environment.
 3. Themethod of claim 1, wherein determining a location of the staticcomputing device comprises determining any of a global location, analtitude, and a floor number.
 4. The method of claim 3, wherein theglobal location, the altitude, and the floor number are stored in theserver.
 5. The method of claim 1, wherein determining the location ofthe static computing device is based on a communication between thestatic computing device and the tracked computing device.
 6. The methodof claim 1, wherein determining the location of the static computingdevice comprises determining a distance between the static computingdevice and the tracked computing device based on a constraint places ona location of the tracked computing device.
 7. The method of claim 6,wherein the constraint is a predefined distance based on a near-fieldcommunication (NFC) between the static computing device and the trackedcomputing device, or based on user input received at the trackedcomputing device, or based on measurements from a RF ranging sensor. 8.The method of claim 1, wherein the information received from the trackedcomputing device is indicative of atmospheric pressure.
 9. The method ofclaim 1, wherein the offset associated with the static computing deviceis determined based on an offset associated with a second staticcomputing device.
 10. The method of claim 9, wherein the offsetassociated with the second static computing device is determined by apressure reference value, and wherein the offset of the static computingdevice is determined from the pressure reference value based on a timecorrelation between the two static computing devices.
 11. The method ofclaim 10, wherein the atmospheric pressure at the static computingdevice is determined based at least in part on averages of the twooffsets of the two static computing devices.
 12. The method of claim 10,wherein the atmospheric pressure at the static computing device isdetermined based on a time correlation between the pressure referenceand the offset associated with the second static computing device andthe offset associated with the static computing device.
 13. The methodof claim 10, wherein the information received from the tracked computingdevice is indicative of an uncorrected atmospheric pressure at thetracked computing device, and wherein the information is corrected basedon the pressure reference value to estimate the atmospheric pressureassociated with the tracked computing device.
 14. The method of claim 1,wherein generating the elevation is equal to the atmospheric pressureassociated with the tracked computing device and the offset associatedwith the static computing device minus an altitude of the staticcomputing device.
 15. The method of claim 1, wherein generating theelevation comprises: determining an elevation constraint between thetracked computing device and the static computing device, the elevationconstraint being based a distance between the static computing deviceand the tracked computing device; determining a cost associated with theelevation constraint, the cost being a function of the elevationconstraint, the atmospheric pressure associated with the trackedcomputing device, the offset associated with the static computingdevice, and an altitude of the static computing device; and determininga minimum value of the cost; and set the elevation based on the minimumvalue.
 16. The method of claim 15, wherein the generating the elevationfurther comprises: determining a second elevation constraint between thetracked computing device and a second tracked computing device; weighingthe second elevation constraint; and updating the cost with the weightedsecond elevation constraint.
 17. The method of claim 15 furthercomprising: adding the minimum value of the cost to a second minimumvalue associated with a second cost, the second cost being associatedwith a second elevation constraint between the tracked computing deviceand a second static computing device; determining that the addition ofthe two minimum values are below a threshold; and updating the offsetassociated with the static computing device based on the determination.18. A computing system for determining an elevation path of a computingdevice in motion in an indoor space and in an outdoor space, thecomputing system comprising: a processor; a memory communicativelycoupled to the processor, the memory bearing instructions that, whenexecuted on the processor, cause the computing system to at least:determine a path associated with the motion of the computing device;determine nodes along the path, the nodes being representative ofendpoints of segments within the path and being associated withelevations of the computing device; classify the nodes between indoornodes and outdoor nodes; add a set of consecutive indoor nodes that havea same elevation value to an indoor segment to generate a plurality ofindoor segments associated with the indoor nodes; add a set ofconsecutive outdoor nodes at a predefined frequency to an outdoorsegment to generate a plurality of outdoor nodes associated with theoutdoor nodes; and generate the elevation path of the computing devicebased on the indoor and outdoor segments.
 19. The computing system ofclaim 18, wherein the indoor and outdoor segments are updated based on avertical acceleration associated with the computing device.
 20. Thecomputing system of claim 18, wherein the indoor and outdoor segmentsare updated based on a velocity associated with the computing device.21. The computing system of claim 20, wherein the velocity is derivedfor a vertical acceleration associated with the computing device. 22.The computing system of claim 20, wherein consecutive indoor segments oroutdoor segments are given a same elevation based on the velocity. 23.The computing system of claim 18, wherein the instructions, whenexecuted on the processor, further cause the computing system to atleast impose a constraint on the addition of the set of consecutiveindoor nodes to the indoor segment and the addition of the set ofconsecutive outdoor nodes to the outdoor segment, the constraintallowing minimum and maximum elevation differences between the nodes ineach set.
 24. A computer readable storage medium comprising instructionsthat, when executed on a computing system configured to determine anelevation path of a computing device in motion in an indoor space and inan outdoor space processor, cause the computing system to at least:determine a path associated with the motion of the computing device;determine nodes along the path, the nodes being representative ofendpoints of segments within the path and being associated withelevations of the computing device; impose a constraint on an additionof consecutive nodes, the constraint allowing minimum and maximumelevation differences between the nodes; add a set of consecutive nodesto a segment of the segments, the addition being based on theconstraints associated with the nodes and the elevations associated withthe nodes or with a predetermined addition frequency; and generate theelevation path of the computing device based on the segments.
 25. Thecomputer readable storage medium of claim 24, wherein the constraint isbased on a type of a node, wherein the type is any of a fixed altitudenode, a fixed floor node, an indoor node, an outdoor node, and anunderground node.
 26. The computer readable storage medium of claim 24,wherein each node is associated with an element of the indoor space orthe outdoor space, wherein the constraint of each node is associatedwith a distance metric between the node and the element, and wherein thedistance metric is based on a type of the node.
 27. The computerreadable storage medium of claim 26, wherein the addition of the set ofconsecutive nodes to the segment comprises updating, for each node inthe set, an elevation of the element and the elevation of the node basedon the constraint.
 28. An elevation path obtained by the process of:determining a path associated with a motion of a computing device in anenvironment; determining nodes along the path, the nodes beingrepresentative of endpoints of segments within the path and beingassociated with elevations of the computing device; imposing aconstraint on an addition of consecutive nodes, the constraint allowingminimum and maximum elevation differences between the nodes; adding aset of consecutive nodes to a segment of the segments, the additionbeing based on the constraints associated with the nodes and theelevations associated with the nodes or with a predetermined additionfrequency; and generating the elevation path of the computing devicebased on the segments.
 29. A computing system for determining anelevation path of a computing device in motion in an indoor space and inan outdoor space, the computing system comprising: a processor; a memorycommunicatively coupled to the processor, the memory bearinginstructions that, when executed on the processor, cause the computingsystem to at least: generate a user interface configured to enter firstinformation indicative of a path associated with the motion of thecomputing device; generate second information indicative of atmosphericpressures at the computing device along the path; transmit the first andsecond information to a server; cause the server to generate theelevation path of the computing device, the elevation path beinggenerated based on elevations determined based on the first and secondinformation and based on constraints imposed by the server onconsecutive points along the path; and present the elevation path at theuser interface.
 30. The computing system of claim 29, wherein theconstraints are imposed based on information associated with the indoorspace and based on information associated with range constraintsassociated with sensors installed along the path.